Rewrite with only sin x and cos x.
sin 3x - cos x

sin 3x - cos x = 3 (sin x)(cos x)(cos x)  -(sin x)(sin x)(sin x) -cos x

Step-by-step explanation:

sin 3x - cos x

This uses Trig Identities.

sin 3x = sin (x + x + x) =  sin (x+x)*cos x + cos (x + x) sin x

= 2sinxcosx * cos x +   [ (cos x)(cos x) -(sin x)(sin x) ] (sin x)

sin 3x - cos x = 2sinxcosx * cos x +   [ (cos x)(cos x) -(sin x)(sin x) ] (sin x) -cos x

sin 3x - cos x = 2sinxcosx * cos x +   sinx (cos x)(cos x) -(sin x)(sin x)(sin x) -cos x

sin 3x - cos x = 3 sinx cosx * cos x  -(sin x)(sin x)(sin x) -cos x

sin 3x - cos x = 3 (sin x)(cos x)(cos x)  -(sin x)(sin x)(sin x) -cos x

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

step-by-step explanation:

given   that triangle lno is congruent to triangle lnm.

we have to fill up the blanks in the given question.

according to above order of congruency   kept in mind we can say that

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

ln ≅ ln due to common in both.

hence, by sas congruency,

the side angle side rule   states that if two sides and the included angle of one triangle are congruent to another triangle, then these two triangles are congruent.